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    <meta name="description" content="难度：困难             题目有效数字（按顺序）可以分成以下几个部分：  一个 小数 或者 整数 （可选）一个 &#39;e&#39; 或 &#39;E&#39; ，后面跟着一个 整数  小数（按顺序）可以分成以下几个部分：  （可选）一个符号字符（&#39;+&#39; 或 &#39;-&#39;） 下述格式之一： 至少一位数字，后面跟着一个点 &#39;.&amp;">
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<meta property="og:description" content="难度：困难             题目有效数字（按顺序）可以分成以下几个部分：  一个 小数 或者 整数 （可选）一个 &#39;e&#39; 或 &#39;E&#39; ，后面跟着一个 整数  小数（按顺序）可以分成以下几个部分：  （可选）一个符号字符（&#39;+&#39; 或 &#39;-&#39;） 下述格式之一： 至少一位数字，后面跟着一个点 &#39;.&amp;">
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            <h1 style="display: none">65_有效数字</h1>
            
            <div class="markdown-body">
              <div class="note note-danger">
            <p>难度：困难</p>
          </div>

<h2 id="题目"><a href="#题目" class="headerlink" title="题目"></a>题目</h2><p>有效数字（按顺序）可以分成以下几个部分：</p>
<ol>
<li>一个 <strong>小数</strong> 或者 <strong>整数</strong></li>
<li>（可选）一个 <code>&#39;e&#39;</code> 或 <code>&#39;E&#39;</code> ，后面跟着一个 <strong>整数</strong></li>
</ol>
<p>小数（按顺序）可以分成以下几个部分：</p>
<ol>
<li>（可选）一个符号字符（<code>&#39;+&#39;</code> 或 <code>&#39;-&#39;</code>）</li>
<li>下述格式之一：<ul>
<li>至少一位数字，后面跟着一个点 <code>&#39;.&#39;</code></li>
<li>至少一位数字，后面跟着一个点 <code>&#39;.&#39;</code> ，后面再跟着至少一位数字</li>
<li>一个点 <code>&#39;.&#39;</code> ，后面跟着至少一位数字</li>
</ul>
</li>
</ol>
<p>整数（按顺序）可以分成以下几个部分：</p>
<ol>
<li>（可选）一个符号字符（<code>&#39;+&#39;</code> 或 <code>&#39;-&#39;</code>）</li>
<li>至少一位数字</li>
</ol>
<p>部分有效数字列举如下：</p>
<ul>
<li><code>[&quot;2&quot;, &quot;0089&quot;, &quot;-0.1&quot;, &quot;+3.14&quot;, &quot;4.&quot;, &quot;-.9&quot;, &quot;2e10&quot;, &quot;-90E3&quot;, &quot;3e+7&quot;, &quot;+6e-1&quot;, &quot;53.5e93&quot;, &quot;-123.456e789&quot;]</code></li>
</ul>
<p>部分无效数字列举如下：</p>
<ul>
<li><code>[&quot;abc&quot;, &quot;1a&quot;, &quot;1e&quot;, &quot;e3&quot;, &quot;99e2.5&quot;, &quot;--6&quot;, &quot;-+3&quot;, &quot;95a54e53&quot;]</code></li>
</ul>
<p>给你一个字符串 s ，如果 s 是一个 有效数字 ，请返回 <strong>true</strong> 。</p>
<h2 id="示例"><a href="#示例" class="headerlink" title="示例"></a>示例</h2><p>示例一：</p>
<blockquote>
<p><strong>输入</strong>：s = “0”<br><strong>输出</strong>：true</p>
</blockquote>
<p>示例二：</p>
<blockquote>
<p><strong>输入</strong>：s = “e”<br><strong>输出</strong>：false</p>
</blockquote>
<p>示例三：</p>
<blockquote>
<p><strong>输入</strong>：s = “.”<br><strong>输出</strong>：false</p>
</blockquote>
<p>示例四：</p>
<blockquote>
<p><strong>输入</strong>：s = “.1”<br><strong>输出</strong>：true</p>
</blockquote>
<h2 id="提示"><a href="#提示" class="headerlink" title="提示"></a>提示</h2><ul>
<li><code>1 &lt;= s.length &lt;= 20</code></li>
<li><code>s</code> 仅含英文字母（大写和小写），数字（<code>0-9</code>），加号 <code>&#39;+&#39;</code> ，减号 <code>&#39;-&#39;</code> ，或者点 <code>&#39;.&#39;</code> 。</li>
</ul>
<h2 id="解题"><a href="#解题" class="headerlink" title="解题"></a>解题</h2><h4 id="确定有限状态自动机"><a href="#确定有限状态自动机" class="headerlink" title="确定有限状态自动机"></a>确定有限状态自动机</h4><p>确定有限状态自动机（以下简称「自动机」）是一类计算模型。它包含一系列状态，这些状态中：</p>
<ul>
<li>有一个特殊的状态，被称作「初始状态」。</li>
<li>还有一系列状态被称为「接受状态」，它们组成了一个特殊的集合。其中，一个状态可能既是「初始状态」，也是「接受状态」。</li>
</ul>
<p>起初，这个自动机处于「初始状态」。随后，它顺序地读取字符串中的每一个字符，并根据当前状态和读入的字符，按照某个事先约定好的「转移规则」，从当前状态转移到下一个状态；当状态转移完成后，它就读取下一个字符。当字符串全部读取完毕后，如果自动机处于某个「接受状态」，则判定该字符串「被接受」；否则，判定该字符串「被拒绝」。</p>
<p>并且如果没有匹配到转移规则，也拒绝该字符串。</p>
<p>自动机驱动的编程，可以看成是一种暴力解法。</p>
<h3 id="合法数值字符串"><a href="#合法数值字符串" class="headerlink" title="合法数值字符串"></a>合法数值字符串</h3><p>一个合法的数值字符串，包含以下部分：</p>
<ul>
<li>符号位，即 +、−两种符号</li>
<li>整数部分，即由若干字符 0−9 组成的字符串</li>
<li>小数点</li>
<li>小数部分，其构成与整数部分相同</li>
<li>指数部分，其中包含开头的字符 e（大写小写均可）、可选的符号位，和整数部分</li>
</ul>
<p>上面五个部分每个都不是必需的，但是受一些额外规则制约：</p>
<ul>
<li>如果符号位存在，其后面必须跟着数字或者小数点</li>
<li>小数点的前后两侧，至少有一侧是数字</li>
</ul>
<h3 id="自动机状态转换"><a href="#自动机状态转换" class="headerlink" title="自动机状态转换"></a>自动机状态转换</h3><p>根据这些规则，罗列出自动机的所有状态：</p>
<ol start="0">
<li>初始状态</li>
<li>符号位</li>
<li>整数部分</li>
<li>左侧有整数的小数点</li>
<li>左侧无整数的小数点</li>
<li>小数部分</li>
<li>字符 e</li>
<li>指数部分的符号位</li>
<li>指数部分的整数部分</li>
</ol>
<p><img src="https://gitee.com/accept_one_time/pic-bed/raw/master/img/20220129144707.png" srcset="/xt-blog/img/loading.gif" lazyload alt="fig1"></p>
<p>初始状态即状态0，接受状态为状态2、状态3、状态5、状态8。</p>
<ul>
<li>当输入正负号时：<ul>
<li>如果当前状态是初始状态0，则状态切换为1</li>
<li>如果当前状态是状态6，则切换到状态7</li>
<li>其他则拒绝</li>
</ul>
</li>
<li>当输入数字时：<ul>
<li>如果当前状态是状态0，1，2，则切换到状态2</li>
<li>如果当前状态是状态3，4，5，则切换到状态5</li>
<li>如果当前状态是状态6，7，8，则切换到状态8</li>
</ul>
</li>
<li>当输入小数点时：<ul>
<li>如果当前状态是状态0，1，则切换到状态4</li>
<li>如果当前状态是状态2，则切换到状态3</li>
<li>其他则拒绝</li>
</ul>
</li>
<li>当输入字符 E | e 时：<ul>
<li>如果当前状态是 2，3，5，则切换到状态6</li>
<li>其他则拒绝</li>
</ul>
</li>
<li>其他字符：<ul>
<li>拒绝 </li>
</ul>
</li>
</ul>
<figure class="highlight java"><table><tr><td class="gutter"><div class="code-wrapper"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span 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class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br></pre></div></td><td class="code"><pre><code class="hljs java"><span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">boolean</span> <span class="hljs-title">isNumber</span><span class="hljs-params">(String s)</span></span>&#123;<br>  <span class="hljs-keyword">int</span> state = <span class="hljs-number">0</span>;<br>  s = s.trim(); <span class="hljs-comment">// 去除头尾空格</span><br>  <span class="hljs-comment">// 遍历所有字符，当作输入</span><br>  <span class="hljs-keyword">for</span> (<span class="hljs-keyword">int</span> i=<span class="hljs-number">0</span>; i&lt;s.length(); i++)&#123;<br>    <span class="hljs-keyword">switch</span> (s.charAt(i)) &#123;<br>        <span class="hljs-comment">// 正负号</span><br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;+&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;-&#x27;</span>:<br>        <span class="hljs-keyword">if</span> (state == <span class="hljs-number">0</span>)&#123;<br>          state = <span class="hljs-number">1</span>;<br>        &#125;<span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (state ==<span class="hljs-number">6</span>)&#123;<br>          state = <span class="hljs-number">7</span>;<br>        &#125;<span class="hljs-keyword">else</span> &#123;<br>          <span class="hljs-keyword">return</span> <span class="hljs-keyword">false</span>;<br>        &#125;<br>        <span class="hljs-keyword">break</span>;<br>        <span class="hljs-comment">// 数字</span><br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;0&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;1&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;2&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;3&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;4&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;5&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;6&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;7&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;8&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;9&#x27;</span>:<br>        <span class="hljs-keyword">if</span> (state==<span class="hljs-number">0</span>||state==<span class="hljs-number">1</span>||state==<span class="hljs-number">2</span>)&#123;<br>          state = <span class="hljs-number">2</span>;<br>        &#125;<span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (state==<span class="hljs-number">3</span>||state==<span class="hljs-number">4</span>||state==<span class="hljs-number">5</span>)&#123;<br>          state = <span class="hljs-number">5</span>;<br>        &#125;<span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (state==<span class="hljs-number">6</span>||state==<span class="hljs-number">7</span>||state==<span class="hljs-number">8</span>)&#123;<br>          state = <span class="hljs-number">8</span>;<br>        &#125;<span class="hljs-keyword">else</span> &#123;<br>          <span class="hljs-keyword">return</span> <span class="hljs-keyword">false</span>;<br>        &#125;<br>        <span class="hljs-keyword">break</span>;<br>        <span class="hljs-comment">// 小数点</span><br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;.&#x27;</span>:<br>        <span class="hljs-keyword">if</span> (state==<span class="hljs-number">0</span>||state==<span class="hljs-number">1</span>)&#123;<br>          state = <span class="hljs-number">4</span>;<br>        &#125;<span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (state==<span class="hljs-number">2</span>)&#123;<br>          state = <span class="hljs-number">3</span>;<br>        &#125;<span class="hljs-keyword">else</span> &#123;<br>          <span class="hljs-keyword">return</span> <span class="hljs-keyword">false</span>;<br>        &#125;<br>        <span class="hljs-keyword">break</span>;<br>        <span class="hljs-comment">// E e</span><br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;E&#x27;</span>:<br>      <span class="hljs-keyword">case</span> <span class="hljs-string">&#x27;e&#x27;</span>:<br>        <span class="hljs-keyword">if</span> (state==<span class="hljs-number">2</span>||state==<span class="hljs-number">3</span>||state==<span class="hljs-number">5</span>)&#123;<br>          state=<span class="hljs-number">6</span>;<br>        &#125;<span class="hljs-keyword">else</span> &#123;<br>          <span class="hljs-keyword">return</span> <span class="hljs-keyword">false</span>;<br>        &#125;<br>        <span class="hljs-keyword">break</span>;<br>      <span class="hljs-keyword">default</span>:<br>        <span class="hljs-keyword">return</span> <span class="hljs-keyword">false</span>;<br>    &#125;<br>  &#125;<br>  <span class="hljs-comment">// 返回接受状态</span><br>  <span class="hljs-keyword">return</span> state==<span class="hljs-number">2</span>||state==<span class="hljs-number">3</span>||state==<span class="hljs-number">5</span>||state==<span class="hljs-number">8</span>;<br>&#125;<br></code></pre></td></tr></table></figure>


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